Squaring device



Feb. 10, 1953 1. A. GREENWOOD, JR

SQUARING DEVI CE Filed April 22, 1950 i 3nventor [1494/ 19. ezwwoao /r-.

RLQIB Q Q 3 Al iv L 3 k 3 \w a & M

(Ittorneg Patented Feb. 10, 1953 SQUARING DEVICE Ivan A. Greenwood, J12, Pleasantville, N. Y., as-

signor, by mesne assignments,

to Librascope,

Inc, a corporation of California Application April 22, 1950, Serial No. 157,434

8 Claims.

This invention pertains to computers in which the input and output data are represented by magnitudes of motions of mechanical parts connected together mechanically, and more specifically to devices for determining squares and square roots.

This invention provides means to solve the equation Yam (1) in which n is any positive or negative integer and in which a: is the independent variable. One unit of the invention solves this equation with n placed equal to 1, two units are required for solution when n equals 2, and in general in units are required for solution. When n is positive, the

means of the invention solves for powers of x, and when n is negative, the solution is for roots of Obviously, the simplest cases, when n=1 or -1, are those in which such a device will find the most application.

One of the best methods of squaring heretofore known and at present largely used, employs a mate its theoretical performance. It is made of a few simple components, and it is completely reversible, so that input data can be applied to either input or output connection point without any change in design oradjustment, the

remaining connection point furnishing the output data.

The apparatus of this invention consists simply of two discs, one driving the other in 2:1 ratio.

- Each disc is attached to a Scotch yoke .or other device for deriving from its rotation the cosine thereof. The resulting displacements of the Scotch yokes are in square relation and may he indicated on properly disposed linearly divided scales.

In operation, an input quantity is applied to I displace one of the Scotch yokes and the dis placement of the other Scotch yoke is then either thesquare or the square root of the input quantity, depending upon the relative proportions of the components.

One purpose then of this invention is to provide a mechanism for mechanically and continuously computing the square of a quantity.

Another purpose is to provide a mechanism for mechanically and continuously computing the square root ofaquantity.

Still another purpose of this invention is to provide a mechanical computer, consisting of a plurality of units connected in tandem, having a plurality of output displacements which are the second, fourth, eighth, etc. powers or roots of the input displacement.

A further understanding of this invention can be gained from the detailed description together with the drawings, in which:

Fig. 1 is a schematic illustration of a iormof the invention employing Scotch yokes and longitudinal scales. r

Fig. 2 is a schematic illustration depicting planetary gear mechanisms and rotary dial scales.

Referring now to Fig. 1, a disc H is arranged to revolve around'its center [2 and carries a pin 1 3 fixed in one face. A Scotch yoke hi surrounds the pin [3 and slides longitudinally in the slide hearing it. The lower .endof. the Scotch yoke carries a pointer I! for indication of. the: yoke displacement upon a scale l8. This scale has a center zero corresponding to the position of the pin [3 when it is displaced from" its topmost position, as depicted. As is well known, in such an arrangement the linear displacement of the pointer ll upon the scale it is directly proportional to'the cosine of the angulardi'sp'lacement of the disc ll, the zero angle position thereof being with the pin (3 at its topmost position for the scale indications shown.

Let it be considered that the independent variable to be applied to the squaring device is in the form of a mechanicaldisplacement datum, which is applied by any means, as for example, manually, by displacing the Scotch yoke it until the pointer ll indicates. upon the scale 53 the magnitude of the displacement datum. It is then obvious that theinput displacement is proportional to cos when o i the angle through which the disc ii is caused toturn by movement of the Scotchyoke, 6 being measured from its zero pcsi tion at the top of the disc. Calling he inde pendent input variable x, then zc=cos (2) In the disc H the dashed circle l9 represents any position of the pin I3 corresponding to an input datum magnitude. The cosine of the angle subtended at the center by the sides AC and BC of the triangle ABC is then the ratio radius therein equalling one-half of the pitch radius of the internal gear teeth 52. At a point 56 on the periphery of the planet gear 53 a pin is provided on which is pivoted an output bar 51, which is restricted by a slide bearing 58 to longitudinal motion. The extent of this motion is arranged to be exactly one-half that of the pin 39 in disc 33 by making the pitch diameter of the internal gear 52 one-half that of the internal gear 34. The relations of Equation 6 then apply in this case equally with the case employing Scotch yokes; that is, the linear displacement of the output bar 51 is for any angular displacement 5 of the disc 33 proportional to one-half of the cosine of 2gb, and the corresponding displacement of the bar 41 is proportional to cos The output bar 51 is provided with a rack 59 and an associated pinion 6|. To this pinion hi there is fixed a dial 62 bearing a scale and having an associated fixed pointer 63. Obviously, to represent a cosine function this scale should have a center zero and extremes of and but in order to carry out the purposes of this inven tion the scale is displaced endwise so that zero is at one end, corresponding to the lowest position of the pin 56, and the other end of the scale represents +1. This is tantamount to adding to Equation 6, unity distance being taken a the pitch radius of the internal gear teeth 34 of the disc 33, so that the resulting relation is represented by Equation 7. This leads to an equality with cos as shown in Equation 8 so that magnitudes of linear displacement of the bar 4| and corresponding angular displacements of the pinion 44 and dial 4! cause magnitudes that are the square thereof respectively in the linear movement of the output bar 51 and in the rotational movements of the pinion 6| and dial 6 2. This is represented by Equation 10:

in which 2/ is the indication on scale 62 and x is the indication on scale 41.

It is obvious that the pinions 44 and BI can be made large so that the scales upon the associated dials 41 and 62 are 360 or less in length. On the other hand, either or both of the pinions can be made smaller, so that the scales upon either or both of the dials 41 and 62 have lengths greater than 360, with any well-known methods employed for indicating quantities upon muiti-turn scales. Thus greatly expanded scales can be employed to enhance the accuracy of utilization of the invention.

It is obvious that for quantities within the scope of the scale 62 this device is reversible, so that inputs applied to the pinion 61 cause outputs at the pinion 44 and indicated upon the dial 41 that are square roots of the inputs. It is true in this embodiment as well as in others that in securing square roots an ambiguity exists, there being two equal values of opposite sign of each root. This ambiguity is inherent in the mathematical basis of any such device and must be resolved by external means.

What is claimed is:

l. A device for solving the equation y= where n is plus or minus unity comprising, means for introducing an input quantity in terms of a displacement magnitude, means for securing the arc cosine function of said displacement magnitude, means for multiplying said are cosine function by 2" to yield a product, and means for ob- 6 taining the cosine of said product as a displacement.

2. A device for obtaining the square of an input quantity comprising, means mechanically displaced in proportion to said input quantity, means producing a second mechanical displacement proportional to the arc cosine of said first mentioned displacement, multiplying means producing a third displacement which is twice that of said second displacement, means for obtaining the cosine of said third displacement, an indicator operated by said last mentioned means and a. scale cooperating with said indicator.

3. A device for solving the equation y= m comprising, means mechanically displaced by an input quantity a, means for producing a second displacement equal to the arc cosine of said input quantity, means for producing a third displacement equal to one-half of said second displacement, means'for producing a fourth displacement equal to the cosine of said third displacement, an indicator actuated by said last mentioned means, and a linear scale adjacent thereto for indicating the magnitude of said fourth displacement representing y.

4. A device for determining squares and square roots comprising, means for converting an input quantity to a rectilinear displacement propor tional thereto, means including a first disc for converting said rectilineardisplacement to an angular displacement equal to the arc cosine of said rectilinear displacement, a second disc, driving means interconnecting said first and second discs and driving said second disc in a two to a one ratio in accordance with the rotation of said first disc,'means including said second disc for producing a rectilinear displacement which is a cosine function of the annular displacement of said second disc, and output means operated by said last mentioned means.

5. A device for solving the equation y=rt in which either variable may constitute the output determined in accordance with an input which consists of the remaining variable comprising, a first member constrained for longitudinal movement, a first rotatable element operatively associated therewith and rotated by an amount which is an arc cosine function of the longitudinal movement of said first member, a second rotatable element operatively associated with said first rotatable member and rotated by an angular amount which is twice that of said first rotatable element, a second member constrained for longitudinal movement operatively associated with said second rotatable element and longitudinally displaceable by an amount which is a cosine function of the angular rotation of said second rotatable element, means for applying a selected input to one of said longitudinally movable members and means for deriving an output from the other of said longitudinally movable members.

6. A squaring device comprising, an input, a link member constrained for longitudinal movement operated by said input, a rotatable element connected to said link element and rotated thereby through an angle which is an arc cosine function of the movement of said link member, a second rotatable element operatively associated with said first mentioned rotatable element and retated thereby through an angle which is twice that through which said first mentioned rotatable element is revolved, a second link member constrained for longitudinal movement connected to said second rotatable element and longitudinally moved thereby through a distance which ing said second gear member to rotate through twice the angle of said first mentioned gear member, a pin mounted on said second gear member extending parallel to the axis thereof at a distance from said axis one-halfthat between the axis of said first mentioned gear memberand the pin mountedthereon, a first Scotch yoke con- .strainedior longitudinal movement having a crosshead engaging the .pin mounted on said first gear member, a second Scotch yokeconstrained for longitudinal movement having a crosshead engaging the .pin mounted on said second gear member, saidpinshavingzero relative phase displacement at one limit of the longitudinal movement or said firstand second Scotch yokes. an

output connected to one of said Scotch yokes and an input connected to theother of said Scotch yokes.

8. A function computing devicecomprising, first bar, a slide'bearing forrestricting. thebar to longitudinal motion, a first rotatable member having internal gear teeth, a first planetary gear meshed with said internal gear teeth and journalled in said first member at a radius equalling one-half of the pitch radius of the internal gear teeth, a bearing fixed in said first planetary gear at a radius equalling .the pitch radius thereof,

ajournal in said first bar operatively associated with said bearing, a second member having internal gear teeth, means 'for drivingly connecting said firstand second membersin 1:2 ratio, a second planetary gear meshed with the internal teethof said se'cond'di's'c and journalled thereon ata radius equalling one-half of the pitch radius of the internal teeth thereof and also one-half of the radius of said first planetary gear, a second hearing fixed in said second planetary gear at a radius equalling the pitch radiusther'eof, asec ond bar havinga journa1 operatively associated with said second bearing, a second slide bearing for restricting said second bar to longitudinal motion, said'first andsecond bearings havin zero relative phase displacement at one limit of longitudinal movement of said first and second bars, an input connected to-one of said bars and an output connected to the other of said bars.

IVAN a. GREENWGOD, JR.

earnestness crrm) The following references are of record in the file of this patent:

UNITED STATES PATENTS 

